Electronic Journal of Differential Equations,
Vol. 2004(2004), No. 59, pp. 1-30.
Title: Damped second order linear differential equation with
deviating arguments: Sharp results in oscillation properties
Authors: Leonid Berezansky (Ben-Gurion Univ. of the Negev, Israel)
Yury Domshlak (Ben-Gurion Univ. of the Negev, Israel)
Abstract:
This article presents a new approach for investigating the oscillation
properties of second order linear differential equations with a damped term
containing a deviating argument
$$
x''(t)-[P(t)x(r(t))]'+Q(t)x(l(t))=0,\quad r(t)\leq t.
$$
To study this equation, a specially adapted version of Sturmian Comparison
Method is developed and the following results are obtained:
(a) A comprehensive description of all critical (threshold) states
with respect to its oscillation properties
for a linear autonomous delay differential equation
$$
y''(t)-py'(t-\tau)+qy(t-\sigma)=0, \quad \tau>0,\;\infty